Unai Emery has identified the 24-year-old as a possible replacement for Ramsey, whose deal at the Emirates expires at the end of the season.
Ramsey will become eligible to sign a pre-contract with an overseas club in January if a new deal hasn’t been agreed with the Gunners before then, and Real Madrid have been heavily linked with a move for the Welsh international.
However, Emery could look to offload Ramsey in January to help raise funds for the Napoli’s Zielinski, who is valued at around £30million.
Italian publication Mediaset, as suggested by The Sun, claims Emery sees Zielinski as a player who could enhance the Gunners current squad and add goals from midfield.
The Poland international moved to Napoli from Udinese in 2016 for £14million and has netted 11 goals in 74 appearances since.
Napoli will be desperate to keep Zielinski as they look to dethrone Juventus, who beat them to the Serie A title last season.
It will take a huge bid from Arsenal for Napoli to consider selling Zielinski this January as he still has just under three years left to run on his current deal.